Lumping and Modeling FCC
Reactions
1.0 Introduction
The kinetics modeling of catalytic cracking has been traditionally
based on using a lumping strategy: chemical species with similar
behaviors are grouped together forming a smaller number of “pseudo”
species (Coxson and Bischoff, 1987).
Commercial
FCC
feedstocks
usually
contain
thousands
of
chemical species with a wide distribution of boiling temperatures. Even
the cracking of gasoline range hydrocarbons can include a quite wide
distribution of molecular weights, from C1 to C20. Thus, lumping of
species is important to make the kinetic modeling a tractable exercise.
In general, there are two basic techniques in lumping the
catalytic cracking of VGO. The first method is to lump molecules in
different distillation cuts “pseudo-species” and to consider chemical
reactions between these lumps. These lumps are usually the feedstock
and the final cracking products, like gasoline, LCO, light gases, and
coke. The second approach is to lump different products based on
main chemical families such as paraffins, olefins, naphthenes, and
aromatics. With this approach important reaction data such as the
reaction type (cracking, hydrogen transfer, or condensation) and
stoichiometry can be included. It is worth mentioning that the second
1
approach can be used to describe the different reaction pathways
(Pitault et al, 1994).
In this respect, the first lumping model proposed was the three
lump model advanced by Weekman and Nace (1970). The three lumps
was later modified, by Yen et al., (1987), proposing a more sound
approach with four lumps where coke and gases were separated. A
more complicated and detailed lump model (10-lumps) describing in
more detail the feedstock was proposed by Jacob et al., (1976). The
10-lump model is of special importance to FCC model development
since its rate constants should not depend, in particular, on the
feedstock composition.
Regarding product distribution, gas composition was reported in
detail by a model developed by John and Wojciechowski in 1975.
Propylene, n-butane, and butene were considered both primary and
secondary products. However, coke, methane, ethane, ethylene, and
iso-butane were postulated as secondary products only. This model
was modified later on by Corma et al (1984) by considering propane
and isobutene as both primary and secondary products.
Takatuska et al (1987) used a six lumps model including the
heavy feedstock (vacuum reside), the vacuum gas oil (VGO) and the
heavy cyclic oil (HCO), the light cyclic oil (LCO), the gasoline, the light
gases, and the coke.
In 1990 (Kraemer et al.,), proposed an eight lump model. The
feedstock was separated into heavy and light fractions: a) heavy
paraffins, heavy naphthenes and heavy aromatics with boiling point in
2
the 343C+ range and b) light paraffins, light naphthenes, and light
aromatics with boiling points in the 220C to 343C range. It was
assumed that the heavy oil lumps can crack into light oil lumps,
gasoline, and light gases and coke. It was also considered that the
light gas oil lump can form gasoline, light gases and coke. It was
hypothesized that gasoline can crack, in turn, into light gases and
coke. The more restricted number of kinetic parameters make this
model more tractable.
There was during the 90’s an attempt to develop a second
generation of lumping models based on reaction mechanisms and
elementary steps (Liguras and Allan, 1990). Froment and co-workers
also proposed single event models involving a detailed description of
VGO catalytic cracking (Vynckier and Froment, 1991; Feng et al.,
1993). This model considered, between other factors a mechanism
including carbenium ions. However, the second generation of FCC
models had many drawbacks given the extensive computational
calculations. Furthermore, several important reactions like hydrogen
transfer and coke formation were not included and this caused major
predication problems.
In 1994, Pitault at al., proposed a model where lumps were
classified by chemical family (e.g. paraffins, olefins, naphthenes, and
aromatics) and molecular weight or boiling range. This approach was
applied to the light gases, gasoline, LCO and feedstock cuts. It has to
be emphasized that this model has the flexibility of being able to
include
important
reactions
like
coking
and
hydrogen
transfer.
Reaction order and stoichiometry for the different lumps reaction were
defined and examined with experimental data.
3
2.0- The Three Lump Model
The three lump model consists of one a feedstock lump ( gas oil,
VGO or any other heavy feed) and two product lumps: a) gasoline b)
coke + light gases. The gasoline lump contains the fraction between C 5
up to the hydrocarbons with a 220C boiling temperature. The coke +
light gases lump contains in addition to coke, C4 and lighter than C4
hydrocarbons. This model can be represented as follows:
Gasoline
k T1
1
Gas oil
k T3
k T2
Light gases&coke
The three lump model.
The reaction order assigned to the three lumps based on the
crackabilities of different lump pseudospecies. Since the feedstock
(VGO or gas oil) contains a mixture of several thousands compounds
of widely different properties, it was suggested that a second order
should be assigned to the cracking of VGO (Weekman and Nace;
1970). However, since gasoline contains a restricted range of
molecular weight hydrocarbons (C5 to C12), it was argued that a first
order should be given to the gasoline cracking (Weekman and Nace;
1970). This assignment of reaction orders is still recommended by
many researchers (Corma and Martinez-Triguero, 1994; Sedran ,
1994).
4
Based on these assumptions the following equations can be
considered:
a-) gas oil cracking can be represented as;
2
r go k T0 φ1 C go
b-) gasoline formation can be modeled as;
2
r g k T1 φ1 C go k T3 φ 2 C g
c-) light gases and coke can be represented as;
r C k T2 φ1 C go 2 k T3 φ 2 C g
It can be stated that numerous experimental and analytical
studies have been developed using the three lump model (Shah et al.,
1977; Paraskos et al.,1976; Corella et al., 1986). In 1971, Nace et al.,
reviewed the three lump model for a large number of feeds and
examined the influence of feed composition on the kinetic rate
constants and on the deactivation of the FCC catalysts. These authors
concluded (Table 2.1) that the overall VGO cracking rate constant is
much larger than the gasoline cracking rate constant for different VGO
composition. Nace et al., (1971) reported for instance, that increasing
the ratio of paraffins to naphthenes led to a decrease in the rate of
gasoline formation and to gasoline overcracking, and to increased
catalyst deactivation. These authors also reported that, whereas the
rate of reaction can vary by a factor of 4, in the range of composition
studied, gasoline selectivity did not seem to vary substantially.
In 1978, Wojciechowski et al., carried out an experimental study
on the cracking activity and the gasoline selectivity of two different
catalysts in which one contained LaX and the other contained LaY
zeolites.
These
authors
carried
5
out
their
work
at
different
temperatures. They concluded that LaY catalyst had higher activity
and better gasoline selectivity than LaX. By referring to their results, it
can be inferred that the gasoline overcracking rate constant was
negligible while compared to the VGO cracking rate constant.
Table 2.1. The three lump model rate constants for different VGO
compositions. kT1, kT2, kT0, kT3 represent the gasoline formation rate
constant, the coke and gases formation rate constant, the overall VGO
cracking rate constant, and the gasoline overcracking rate constant
respectively (Nace et al., 1971).
Kinetic rate constants at 900 _F (hr-1)
kT1
kT3
kT2/kT1 kT3/kT1
Charge Stock
kT0
P1
231.8
26.3
1.83
0.83
0.06
P2
232.7
26.2
1.09
0.80
0.03
P3
334.0
28.0
1.86
0.82
0.05
N1
139.2
33.5
1.54
0.85
0.04
N2
234.2
29.4
2.35
0.86
0.07
N3
236.2
31.0
2.02
0.85
0.06
PN33
236.4
30.9
1.94
0.85
0.05
PA31
324.7
21.0
2.87
0.85
0.12
PA32
322.9
18.6
1.95
0.81
0.09
PA33
322.1
17.6
1.48
0.80
0.07
PA331
315.5
12.6
2.66
0.81
0.17
PA34
322.1
17.8
1.78
0.81
0.08
PA37
310.3
7.71
2.18
0.75
0.21
PA38
321.1
16.6
1.66
0.79
0.08
AA45
412.3
9.3
2.28
0.76
0.19
PC32
319.3
15.0
1.15
0.78
0.06
6
In 1984, Corma et al., conducted an experimental work to investigate
the kinetic of VGO cracking on RE-HY zeolite using a fixed bed
microreactor. According to these results (Table 2.2), at 524C, the
ratio of the gasoline overcracking rate constant to the VGO cracking
rate constant is very small (0.006).
In 1986 Corella et al., applied the three lump models to study
the kinetics of VGO cracking in a FCC pilot plant unit. These authors
were able to develop a kinetic model claiming that this model was able
to simulate the commercial FCC units.
In 1988, Kramer and de Lasa studied the kinetics of the
paraffinic VGO cracking under operating conditions similar to those
found in commercial risers. On the basis of the three lump model and
the assumption that the riser simulator operated as a batch reactor,
they were able to develop a reliable model to predict the paraffinic
VGO
conversion.
Reported
kinetic
constants
at
two
different
temperatures are shown in Table 2.3. In this study, the gasoline
cracking rate constant was assumed to be zero and this was consistent
with previous studies.
2.1-The Four Lump Model
In 1987, Yen et al. introduced the four lump model splitting the
light gases + coke lump in two separate lumps: a) coke and b) light
gases. These authors used a second order reaction for VGO cracking.
The kinetic parameters were determined from riser pilot plant data and
were
correlated
with
feedstock
7
characteristics,
and
operating
conditions. This model is claimed to predict very effectively the coke
yield for VGO cracking in FCC pilot plants and commercial units.
Table 2.2: Calculated values for the kinetic constants of
reaction scheme. kT0, kT1, kT2, kT3 represent the overall
rate constant, the gasoline formation rate constant, the
formation rate constant and the gasoline overcracking
respectively (Corma et al., 1984).
kT0
kT1
kT2
kT3
(h-1)
(h-1)
(h-1)
(h-1)
x
x
x
x
10-5
10-5
10-5
10-2
480 _°C
503 _°C
2.91
2.44
0.47
16.21
5.14
4.21
0.93
30.71
524 _°C
11.07
8.96
2.11
65.82
Table 2.3: Calculated values for the kinetic constants of
reaction scheme. kT0, kT1, kT2, kT3 represent the overall
rate constant, the gasoline formation rate constant, the
formation rate constant and the gasoline overcracking
respectively (Kramer and de Lasa, 1988).
T, _°C
500
550
kT0
4.11
5.03
kT1
3.04
3.12
kT3
0.00
0.00
*Units of kT0, kT1, and kT2 are 1/(g of oil-g of catalyst-s).
Unit of kT3 are 1/(g of catalyst-s).
8
the triangular
VGO cracking
gas and coke
rate constant
the triangular
VGO cracking
gas and coke
rate constant
kT2
1.07
1.91
In 1994 Gianetto et al. studied the effect of the crystal size of the Yzeolite on gasoline composition. They used the Riser Simulator to carry
out their experimental work. A four lump model was applied as
follows:
Light gases
k
VGO
(A)
31
k 21
k 11
Gasoline (B)
k
k 32
22
Coke
where the rates of gasoline formation and gasoline consumption were
described as,
a-) gas oil consumption rate
 rgo  k 11φC 2go
b-) gasoline formation rate
rg  k11φC 2go  φ(k 21  k 22 )C g
c-) light gases formation rate
rlg  k 31φC 2go  k 21φC g
d-) coke formation rate
rc  k 32 φC 2go  k 22 φC g
These authors found that the zeolite catalysts with small crystals
were moderately more active than those with large crystals. Moreover,
they pointed out that the gasoline overcracking was negligible for both
small crystal zeolites and large crystal zeolites, since the calculated
constants were very small.
In 1994, Farag et al. studied the effect of the addition of metal
traps in the FCC catalysts. Experimental runs were performed in a
microcatalytic fixed bed reactor. It was concluded that the addition of
9
the metal traps was beneficial for the gasoline yield and research
octane number. The four lump model was used to evaluate the kinetics
constants. The equations developed from the four lump model were
also reliable to evaluate the adsorption constants for VGO, gasoline,
and light gases. It was also reported that the values for the kinetic
constants for the cracking of gasoline to coke and light gases were
very close to zero.
More recently Ali and Rohani (1997) developed a simple dynamic
model to describe the dynamic behavior of the FCC unit (riserregenerators and their interactions). The four lump model was
employed to simulate the cracking reactions. Their model was able to
simulate the data of an industrial scale unit reasonably well.
Juarez et al., (1997) extended the four lump model to five
lumps. These authors further divided the gases lump into two different
lumps: a) dry gas, b) liquefied petroleum gas (LPG). Note that LPG can
be formed either directly from gas oil or as a secondary product from
gasoline overcracking. On the other hand, dry gas (H2, C1, C2) can be
formed either directly from gas oil cracking or as a secondary product
from gasoline and LPG cracking. The five lump model can be
schamatically represented as:
10
VGO
Coke
Gasoline
Dry gas
LPG
The five lump model
2.2 Catalyst Deactivation
Catalyst deactivation in FCC process can take place due to
several factors. Catalyst pellets can lose its shape or mass due to
attrition and high temperatures (sintering). Catalyst poisoning can also
take place given the effect of impurities contained in the feedstock.
Typical contaminants are hydrocarbons containing S, N, O, Ni and V
(Larocca, 1988; Larocca et al., 1990; Farag, 1993).
However, under normal FCC conditions coke is the most
important factor affecting catalyst activity. As catalytic reactions
proceed coke deposits on the catalyst surface. Coke covers the
catalyst active sites leading to catalyst activity decay.
11
In this respect, important modelling efforts have been addressed
to model catalyst deactivation due to coke. These models are reviewed
in the following section.
2.2.1-Catalyst activity decay functions
Two main approaches have been used, so far, to represent the
effect of coking phenomena on catalyst decay. The first approach uses
the catalyst coke content (Froment and Bischoff, 1961; 1962). The
second approach relates catalyst deactivation to time-on-stream (TOS)
(Wojciechowski, 1968;1974).
2.2.1.1-Decay model based on time-on-stream
The time-on-stream decay model (TOS) represents a first
approach to catalyst deactivation. This approach assumes that the
coking rate
is
independent of reactant
composition,
extent of
conversion, and hydrocarbon space velocity (Yates.,1983).
In this respect, Weekman (1968) employed to describe catalyst
deactivation, the following two simple relations;
a)- exponential decay law = exp (-t)
b)- power decay law
= t-n
(2.7.4.a)
(2.7.4.b)
where t represents catalyst time-on-stream,  and n are rate
constants of the catalyst decay function.
12
Regarding TOS models, Szepe and Levenspiel (1971) showed
that many deactivation functions could be derived by assuming the
rate of catalyst decay as a function of the number of active sites. Thus,
the rate of catalyst activity decay can be expressed as a function of
the fraction of remaining active sites as follows;
-d /dt =kd 
(2.7.4.c)
n
-d /dt =kd1 C2go 
(2.7.4.d)
where  is the fraction of remaining active sites, t is the catalyst timeon-stream, kd and kd1 catalyst decay constants, n the order of catalyst
activity decay and Cgo is the gas oil feedstock concentration.
Wojciechowski (1974) suggested a more detailed form of the
power law by integrating eq (2.7.4.c) with  =1 at t=0. This yields the
following:
 = [1+ kdt(n-1)]-N
(2.7.4.e)
It should be mentioned that this form of deactivation function
has been widely used in the literature being able to represent both gas
oil
cracking
(Campbell
and
Wojciechowski,
1971;
John
and
Wojciechowski,1975) and cracking of model compounds (Corma and
Wojciechowski.,1984, Abbot and Wojciechowski, 1987; Kennedy et
al,1991).
Regarding the exponential form of the deactivation function
(=exp(-t)) it has also been used frequently in the technical
literature. Kraemer et al (1987,1990) employed this form to represent
13
gas oil cracking in a CREC Riser Simulator. Liguras and Allen (1989)
used this equation to describe the cracking of model compounds using
an amorphous silica-alumina-zirconia catalyst. Ali and Rohani (1997)
also used the exponential decay function in the case of a dynamic
model for FCC units.
More recently, a modified exponential function, =exp(-tn) was
considered. This empirical relation was used to represent activity
decay for the cracking of 2-methylpentane on USY zeolite (Babitz et
al., 1997). It was found that the 0.4 value was adequate for the “n”
parameter. Hopkins et al (1996), used the same equation with n=0.5
and this for the modeling of catalytic activity decay while cracking
hexane.
2.2.1.2- Decay model based on coke content
To provide, however, a more sound approach to catalyst decay,
the catalyst deactivation function () was related to the coke content
Cc. With this end, several forms are proposed in the technical literature
as follows (Froment and Bischoff , 1962 and 1979);
a) = exp (-Cc)
(2.7.4.f1)
b) =1/(1+Cc)
(2.7.4.f2)
c) =1/(1+Cc)2
(2.7.4.f3)
d) =1-Cc
(2.7.4.f4)
e) =(1-Cc)2
(2.7.4.f5)
where  is a constant which can be found by fitting the experimental
data.
14
Another alternative deactivation function based on coke content
was proposed by Gross et al (1974). In this function the effect of coke
content was expressed with a two parameter function,  and n as
follows;
=1/(1+Ccn)
(2.7.4.g)
Acharya et al., (1989) investigated silica alumina catalyst
deactivation for cumene cracking. It was hypothesized that the coking
reaction takes place as a consecutive step to the main reaction. The
modified deactivation function is based on the observation that after a
very sharp initial activity decline there is a slow activity decay and
finally a stablization on a steady activity level. The proposed
expression is given as;
m=R+(1-R)exp(-Cc)
(2.7.4.h)
where  and R represent a deactivation coefficient, and a residual
activity level respectively. Note that various model parameters of
eq(2.7.4.h) are obtained by nonlinear regression fitting of the
experimental data.
Regarding further efforts on catalyst deactivation, as a function
of coke content (Cc), Forissier and Bernard (1991) suggested an
empirical relation taken into account site coverage, pore plugging, and
diffusion limitations caused by pore plugging. They suggested a
deactivation function with the following form;
=(B+1)/(B+exp(ACc))
15
(2.7.4.i)
where Cc is the catalyst coke content expressed in wt%, A and B are
two
constants
which
are
functions
of
feedstock
composition,
determined by the appropriate fitting of the experimental data.
In this respect, Forissier et al (1991) established a distinction
between catalyst deactivation (1) and coke formation (2) relating
these two functions as follows;
2 = 1 (Cmc-Cc)/Cmc
with Cmc representing
(2.7.4.j)
the maximum coke fraction observed on the
catalyst.
The use of 2 suggests that the coke concentration, Cc, can reach
a limiting level Cmc at the early stages of the reaction. Then coke
formation is halted and a residual activity is available for other
cracking reactions (Pitault et al.,1994).
Corma et al., (1994) studied paraffins catalytic cracking. These
authors suggested that the use of a TOS decay model is not consistent
with a kinetic model in which the product olefins are strongly adsorbed
on the catalyst. To account for this, the following model was
suggested;
d/dt = -kmd m X
(2.7.4.k)
where kmd and m are the decay model parameters and X is the
conversion.
16
In this respect, this model assumed that there is a direct
relationship between coke formation and catalyst deactivation. In fact,
eq (2.7.4.k) can be derived from Froment and co-workers model as
follows;
dCc/dt = r0c 
where
(2.7.4.l)
= exp (-Cc), and r0c is the rate of coke formation. If
coke formation reaction is assumed to be first order and m=2,
equation (2.7.4.l) is obtained.
More recently, a mathematical expression of  versus catalyst
coke content (Cc) was suggested (Van Landeghem et al., 1996). This
model can be expressed as;
d/dCc = F + E (1-)
(2.7.4.m)
where F is proportional to the remaining activity and E is proportional
to the lost activity. Based on these assumptions the following
deactivation function was postulated;
 = (E+F)/(E+F exp[(E+F)Cc])
(2.7.4.n)
where E and F values are adjustable parameters calculated for each
feedstock.
2.3- Conclusions
In conclusion, while the mechanism of coke formation is not yet
well understood, two types of models have been proposed in the
17
technical literature for catalyst deactivation. One of these model is
based on the time-on-stream and this represent a rather rudimentary
approach to catalyst decay modeling. A second approach is to relate
catalyst decay to coke content, being this a more sound mechanistic
description of catalyst decay.
18
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